Finite Group Databasebeta

← Group #300910

Character table — Group #300910

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ911111111111111111-1-1-1-1111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-11111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111-111-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-111-1-1-1-1111-1
χ17222222222-222-2-2-22-22222-2000000000022-2-2-2-20022-2-2000000000000000000000000
χ18222222222-222-2-2-22-22222-20000000000-2-222-2-200-2-222000000000000000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-2000000000022-2-22200-2-222000000000000000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-20000000000-2-222220022-2-2000000000000000000000000
χ2122222222-22-2-2222-2-20000-22222-2-2-2-222000000220000000000000000-2-20000000000
χ2222222222-22-2-2222-2-20000-22222-2-2-2-2-2-2000000-2-20000000000000000220000000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-2222222000000-2-200000000000000002-20000000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-22222-2-2000000220000000000000000-220000000000
χ2522-22-22-2-2-202-2000202i2i−2i−2i022−2−222−2−200002i−2i0000002-2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ2622-22-22-2-2-202-2000202i2i−2i−2i022−2−222−2−20000−2i2i000000-22−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ2722-22-22-2-2-202-2000202i2i−2i−2i0−2−222−2−22200002i−2i0000002-2−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ2822-22-22-2-2-202-2000202i2i−2i−2i0−2−222−2−2220000−2i2i000000-22i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ2922-22-22-2-2-202-200020−2i−2i2i2i022−2−222−2−200002i−2i000000-22i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ3022-22-22-2-2-202-200020−2i−2i2i2i022−2−222−2−20000−2i2i0000002-2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ3122-22-22-2-2-202-200020−2i−2i2i2i0−2−222−2−22200002i−2i000000-22−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ3222-22-22-2-2-202-200020−2i−2i2i2i0−2−222−2−2220000−2i2i0000002-2i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ332-22-222-2-2-20-22000202i−2i2i−2i02−22−22−22−2002i−2i0000002-200i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ342-22-222-2-2-20-22000202i−2i2i−2i02−22−22−22−200−2i2i000000-2200−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ352-22-222-2-2-20-22000202i−2i2i−2i0−22−22−22−22002i−2i0000002-200−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ362-22-222-2-2-20-22000202i−2i2i−2i0−22−22−22−2200−2i2i000000-2200i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ372-22-222-2-2-20-2200020−2i2i−2i2i02−22−22−22−2002i−2i000000-2200i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ382-22-222-2-2-20-2200020−2i2i−2i2i02−22−22−22−200−2i2i0000002-200−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ392-22-222-2-2-20-2200020−2i2i−2i2i0−22−22−22−22002i−2i000000-2200−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ402-22-222-2-2-20-2200020−2i2i−2i2i0−22−22−22−2200−2i2i0000002-200i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ412-2-2-2-222222-2-2-22-22-22-2-222000000000000002-20000002-2-2200002-2-22000000000000
χ422-2-2-2-222222-2-2-22-22-22-2-222000000000000002-2000000-222-20000-222-2000000000000
χ432-2-2-2-222222-2-2-22-22-2-222-2200000000000000-220000002-2-220000-222-2000000000000
χ442-2-2-2-222222-2-2-22-22-2-222-2200000000000000-22000000-222-200002-2-22000000000000
χ452-2-2-2-22222-2-2-22-22222-2-22-22-2-222-2-22000000-2200000000002-2-220000000000000000
χ462-2-2-2-22222-2-2-22-22222-2-22-2-222-2-222-2000000-220000000000-222-20000000000000000
χ472-2-2-2-22222-2-2-22-2222-222-2-22-2-222-2-220000002-20000000000-222-20000000000000000
χ482-2-2-2-22222-2-2-22-2222-222-2-2-222-2-222-20000002-200000000002-2-220000000000000000
χ492-2-2-2-2222-2-2222-22-2-2000022-2-22-222-200000000000000000000000000002-22-2000000
χ502-2-2-2-2222-2-2222-22-2-2000022-2-22-222-20000000000000000000000000000-22-22000000
χ512-2-2-2-2222-2-2222-22-2-200002-222-22-2-2200000000000000000000000000002-2-22000000
χ522-2-2-2-2222-2-2222-22-2-200002-222-22-2-220000000000000000000000000000-222-2000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-440400-4-44000000000000000000000004i−4i0000000000000000000000000000
χ55444-4-4-4-440400-4-4400000000000000000000000−4i4i0000000000000000000000000000
χ56444-4-4-4-440-40044-400000000000000000000000000000000000000000000000002i2−2i200
χ57444-4-4-4-440-40044-40000000000000000000000000000000000000000000000000−2i22i200
χ5844-44-44-4-440-44000-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-44-44-4-440-44000-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-44-444-4-4404-4000-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ614-44-444-4-4404-4000-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ624-4-444-4-4404004-4-4000000000000000000000000000000000000000000000002i2−2i20000
χ634-4-444-4-4404004-4-400000000000000000000000000000000000000000000000−2i22i20000
χ644-4-444-4-440-400-4440000000000000004-4000000000000000000000000000000000000
χ654-4-444-4-440-400-444000000000000000-44000000000000000000000000000000000000
χ664-4-4-4-4444-4444-44-4-440000-40000000000000000000000000000000000000000000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).